The physical uplink control channel (PUCCH) in Long Term Evolution (LTE) carries important control information for the base station to perform upper layer scheduling for higher system capacity. As the standard evolves, LTE specifies PUCCH Format 2/2a/2b beyond Format 1 to carry both channel quality indicator (CQI) and acknowledgment (ACK) bits. CQI is an important parameter for link adaptation and represents the recommended modulation scheme and coding rate that should be used for the downlink transmission. ACK bits are essential for use of hybrid automatic repeat request (HARQ). Joint maximum likelihood detection (MLD) of CQI and ACK bits is desired because of its superior performance compared with a suboptimal detection method. However, the complexity of joint MLD grows exponentially with the number of CQI bits and ACK bits. It can be shown that the complexity is prohibitively high for real-time implementation in digital signal processing (DSP) despite its significant gain over a suboptimal detection method.